With the rising popularity of virtual worlds, the importance of data-driven parametric models of 3D meshes has grown rapidly. Numerous applications, such as computer vision, procedural generation, and mesh editing, vastly rely on these models. However, current approaches do not allow for independent editing of deformations at different frequency levels. They also do not benefit from representing deformations at different frequencies with dedicated representations, which would better expose their properties and improve the generated meshes' geometric and perceptual quality. In this work, spectral meshes are introduced as a method to decompose mesh deformations into low-frequency and high-frequency deformations. These features of low- and high-frequency deformations are used for representation learning with graph convolutional networks. A parametric model for 3D facial mesh synthesis is built upon the proposed framework, exposing user parameters that control disentangled high- and low-frequency deformations. Independent control of deformations at different frequencies and generation of plausible synthetic examples are mutually exclusive objectives. A Conditioning Factor is introduced to leverage these objectives. Our model takes further advantage of spectral partitioning by representing different frequency levels with disparate, more suitable representations. Low frequencies are represented with standardised Euclidean coordinates, and high frequencies with a normalised deformation representation (DR). This paper investigates applications of our proposed approach in mesh reconstruction, mesh interpolation, and multi-frequency editing. It is demonstrated that our method improves the overall quality of generated meshes on most datasets when considering both the $L_1$ norm and perceptual Dihedral Angle Mesh Error (DAME) metrics.

翻译：随着虚拟世界的日益普及，数据驱动的三维网格参数化模型的重要性迅速增长。计算机视觉、程序化生成和网格编辑等众多应用极大地依赖这些模型。然而，当前方法无法在不同频率层级上独立编辑形变，也未能利用不同频率的形变采用专用表示所带来的优势——这些表示能更好地展现形变特性，并提升生成网格的几何质量和感知质量。本文引入谱网格作为一种将网格形变分解为低频形变和高频形变的方法。这些低频和高频形变特征被用于图卷积网络的表示学习。基于所提出的框架，我们构建了一个三维面部网格合成的参数化模型，该模型提供了可控制解耦的高频和低频形变的用户参数。对不同频率形变的独立控制与生成合理合成样本是相互排斥的目标。为此，我们引入了一个条件因子来平衡这两个目标。我们的模型通过采用不同且更合适的表示来表征不同频率层级，从而进一步利用了谱分解的优势：低频采用标准化的欧氏坐标表示，高频采用归一化的形变表示。本文研究了所提方法在网格重建、网格插值和多频编辑中的应用。实验表明，在大多数数据集上，当考虑$L_1$范数和感知性二面角网格误差指标时，我们的方法能提升生成网格的整体质量。